In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another.
For a polyhedron, this operation adds a new hexagonal face in place of each original edge.
The chamfered tetrahedron or alternate truncated cube is a convex polyhedron constructed: For a certain depth of chamfering/truncation, all (final) edges of the cT have the same length; then, the hexagons are equilateral, but not regular.
The cC is a convex polyhedron with 32 vertices, 48 edges, and 18 faces: 6 congruent (and regular) squares, and 12 congruent flattened hexagons.For a certain depth of chamfering, all (final) edges of the chamfered cube have the same length; then, the hexagons are equilateral, but not regular.
The cC is also inaccurately called a truncated rhombic dodecahedron, although that name rather suggests a rhombicuboctahedron.
The DaYan Gem 7 is a twisty puzzle in the shape of a chamfered cube.
[2] In geometry, the chamfered octahedron is a convex polyhedron constructed by truncating the 8 order-3 vertices of the rhombic dodecahedron.
These truncated vertices become congruent equilateral triangles, and the original 12 rhombic faces become congruent flattened hexagons.For a certain depth of truncation, all (final) edges of the cO have the same length; then, the hexagons are equilateral, but not regular.
The chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 12 congruent regular pentagons and 30 congruent flattened hexagons.It is constructed as a chamfer of a regular dodecahedron.
The pentagons are reduced in size and new faces, flattened hexagons, are added in place of all the original edges.
For a certain depth of chamfering, all (final) edges of the cD have the same length; then, the hexagons are equilateral, but not regular.
The cD is also inaccurately called a truncated rhombic triacontahedron, although that name rather suggests a rhombicosidodecahedron.
In geometry, the chamfered icosahedron is a convex polyhedron constructed by truncating the 20 order-3 vertices of the rhombic triacontahedron.
The hexagonal faces of the cI can be made equilateral, but not regular, with a certain depth of truncation.
The chamfer operation applied in series creates progressively larger polyhedra with new faces, hexagonal, replacing the edges of the current one.